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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 32, 1995 - Issue 4
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Original Articles

Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993 Footnote∗

D. Boukari George Washington University,
&
A. V. Fiacco George Washington University,
Pages 301-334 | Published online: 20 Mar 2007

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G. Bigi & M. Passacantando. (2017) Auxiliary problem principles for equilibria. Optimization 66:12, pages 1955-1972.
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V.F. Demyanov & G.Sh. Tamasyan. (2014) Direct Methods in the Parametric Moving Boundary Variational Problem. Numerical Functional Analysis and Optimization 35:7-9, pages 932-961.
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V.F. Demyanov & G.Sh. Tamasyan. (2011) Exact penalty functions in isoperimetric problems. Optimization 60:1-2, pages 153-177.
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V. F. Demyanov. (2005) An old problem and new tools. Optimization Methods and Software 20:1, pages 53-70.
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V.F. Demyanov, G. Di Pillo & F. Facchinei. (1998) Exact penalization via dini and hadamard conditional derivatives. Optimization Methods and Software 9:1-3, pages 19-36.
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Vladimir Norkin. (2024) The exact projective penalty method for constrained optimization. Journal of Global Optimization.
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Risheng Liu, Xuan Liu, Shangzhi Zeng, Jin Zhang & Yixuan Zhang. (2023) Value-Function-Based Sequential Minimization for Bi-Level Optimization. IEEE Transactions on Pattern Analysis and Machine Intelligence 45:12, pages 15930-15948.
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V.I. Norkin. (2022) A new projective exact penalty function for a general constrained optimization. Reports of the National Academy of Sciences of Ukraine:5, pages 23-29.
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Hongbing Zhou, Xianlin Zeng & Yiguang Hong. (2019) Adaptive Exact Penalty Design for Constrained Distributed Optimization. IEEE Transactions on Automatic Control 64:11, pages 4661-4667.
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F Mesa, E Orrego & C Ramirez. (2019) Optimal control with bounded entries principle of Pontryagin. Journal of Physics: Conference Series 1403, pages 012012.
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Vladimir D. Skarin. 2016. Discrete Optimization and Operations Research. Discrete Optimization and Operations Research 441 451 .
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Alexander J. Zaslavski. (2014) An Approximate Exact Penalty for Vector Inequality-Constrained Minimization Problems. Vietnam Journal of Mathematics 42:4, pages 499-508.
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Pablo Lanillos, Eva Besada-Portas, Jose Lopez-Orozco & Jesus de la Cruz. (2014) Minimum Time Search in Uncertain Dynamic Domains with Complex Sensorial Platforms. Sensors 14:8, pages 14131-14179.
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A. J. Zaslavski. (2013) An Approximate Exact Penalty in Constrained Vector Optimization on Metric Spaces. Journal of Optimization Theory and Applications 162:2, pages 649-664.
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Bingzhuang Liu & Wenling Zhao. (2014) New Exact Penalty Functions for Nonlinear Constrained Optimization Problems. Abstract and Applied Analysis 2014, pages 1-6.
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Alexander J. Zaslavski. (2012) An exact penalty approach to constrained minimization problems on metric spaces. Optimization Letters 7:5, pages 1009-1016.
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Alexander J. Zaslavski. (2013) Exact Penalty Property in Optimization with Mixed Constraints via Variational Analysis. SIAM Journal on Optimization 23:1, pages 170-187.
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Liu Bingzhuang & Zhao Wenling. (2012) A modified exact smooth penalty function for nonlinear constrained optimization. Journal of Inequalities and Applications 2012:1.
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Alexander J. Zaslavski. (2011) LOCAL SOLUTIONS OF CONSTRAINED MINIMIZATION PROBLEMS AND CRITICAL POINTS OF LIPSCHITZ FUNCTIONS. Taiwanese Journal of Mathematics 15:5.
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Alexander J. Zaslavski. (2010) An Estimation of Exact Penalty for Infinite-Dimensional Inequality-Constrained Minimization Problems. Set-Valued and Variational Analysis 19:3, pages 385-398.
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A.N. Natali, C.G. Fontanella & E.L. Carniel. (2010) Constitutive formulation and analysis of heel pad tissues mechanics. Medical Engineering & Physics 32:5, pages 516-522.
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Alexander J. Zaslavski. (2010) STABILITY OF EXACT PENALTY FOR NONCONVEX INEQUALITY-CONSTRAINED MINIMIZATION PROBLEMS. Taiwanese Journal of Mathematics 14:1.
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Immanuel M. Bomze, Vladimir F. Demyanov, Roger Fletcher & Tamás TerlakyVladimir F. Demyanov. 2010. Nonlinear Optimization. Nonlinear Optimization 55 163 .
Alexander J. Zaslavski. 2010. Variational Analysis and Generalized Differentiation in Optimization and Control. Variational Analysis and Generalized Differentiation in Optimization and Control 223 232 .
Alexander J. Zaslavski. (2009) Existence and stability of exact penalty for optimization problems with mixed constraints. Nonlinear Analysis: Theory, Methods & Applications 71:7-8, pages 3053-3062.
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Alexander J. Zaslavski. (2009) A sufficient condition for exact penalty functions. Optimization Letters 3:4, pages 593-602.
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Alexander J. Zaslavski. (2007) Existence of Exact Penalty and Its Stability for Nonconvex Constrained Optimization Problems in Banach Spaces. Set-Valued Analysis 16:5-6, pages 673-691.
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Alexander J. Zaslavski. (2008) STABILITY OF EXACT PENALTY FOR CLASSES OF CONSTRAINED MINIMIZATION PROBLEMS IN BANACH SPACES. Taiwanese Journal of Mathematics 12:6.
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Alexander J. Zaslavski. (2007) Exact penalty property for a class of inequality-constrained minimization problems. Optimization Letters 2:3, pages 287-298.
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Adam B. Levy. (2006) Constraint incorporation in optimization. Mathematical Programming 110:3, pages 615-639.
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Alexander J. Zaslavski. (2006) Existence of Exact Penalty for Constrained Optimization Problems in Metric Spaces. Set-Valued Analysis 15:3, pages 223-237.
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Alexander J. Zaslavski. (2007) Existence of exact penalty for constrained optimization problems in Hilbert spaces. Nonlinear Analysis: Theory, Methods & Applications 67:1, pages 238-248.
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Alexander J. Zaslavski. (2007) Existence of Approximate Exact Penalty in Constrained Optimization. Mathematics of Operations Research 32:2, pages 484-495.
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Xuewu Du. (2006) Results on Exactness Properties of the HP-ALF for Inequality Constraints. Results on Exactness Properties of the HP-ALF for Inequality Constraints.
Xuewu Du, Liansheng Zhang & Yuelin Gao. (2006) A class of augmented Lagrangians for equality constraints in nonlinear programming problems. Applied Mathematics and Computation 172:1, pages 644-663.
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Adam B. Levy. (2005) Convergence of Successive Approximation Methods with Parameter Target Sets. Mathematics of Operations Research 30:3, pages 765-784.
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V. F. Demyanov, F. Giannessi & G. Sh. Tamasyan. 2005. Variational Analysis and Applications. Variational Analysis and Applications 301 342 .
Vladimir F. Demyanov & Franco Giannessi. 2003. Equilibrium Problems and Variational Models. Equilibrium Problems and Variational Models 109 134 .
Vladimir F. Demyanov. 2003. Equilibrium Problems and Variational Models. Equilibrium Problems and Variational Models 79 108 .
Gianni Di Pillo & Stefano Lucidi. (2002) An Augmented Lagrangian Function with Improved Exactness Properties. SIAM Journal on Optimization 12:2, pages 376-406.
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V. F. Demyanov, A. Astorino & M. Gaudioso. 2001. Advances in Convex Analysis and Global Optimization. Advances in Convex Analysis and Global Optimization 11 30 .
Werner Oettli, Dirk Schläger & Michel Théra. 2000. Optimization. Optimization 329 338 .
Chih-Jen Lin, Shu-Cherng Fang & Soon-Yi Wu. (1998) An Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming. SIAM Journal on Optimization 8:2, pages 443-456.
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Jong-Shi Pang. (1997) Error bounds in mathematical programming. Mathematical Programming 79:1-3, pages 299-332.
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